Gamma-ray bursts (GRBs) are the mysterious, short and intense flashes of gamma-rays in the space, and are believed to originate from the rare, explosively devastating, stellar events that happens at cosmological distances. Enormous progress has been made from four decades of GRB research endeavor but the ultimate understanding of their origins has yet to arrive. Recently revealed features in their early afterglows broadened the opportunity space for exploration. We have carried out extensive studies on various physical processes in GRBs. We showed that the distribution of electrons' energy spectral index in GRBs and other relativistic sources is inconsistent with the prediction from the first-order Fermi theory of the shock particle acceleration. We investigated the photon scattering processes within the relativistic outflow that produces the GRB and calculated the resultant emission flux from it. We showed the scattering of the GRB prompt photons by the circum-burst dust, although an attractive possibility, can not explain the puzzling plateau component in the GRB afterglow light curve. We made meaningful constraint on the GRB prompt emission radius, R [greater-than or equal to] 10¹⁴, by studying the synchrotron self absorption for a small sample of bursts with good data. We showed that a late jet, which is thought to be producing the late X-ray flares in GRB afterglows, will produce detectable emissions from its interactions with other components in the explosive event of GRB, and identification of these emissions could verify the existence of the late jet and further prove the massive star origin of long-duration GRBs.